Question

Determine if one, both, or neither of the following is a proportion. 168=?2412, 84=?126(1 point)
Responses

Neither is a proportion.
Neither is a proportion.

168=2412, 84=126
Start Fraction 16 over 8 End Fraction equals Start Fraction 24 over 12 End Fraction , Start Fraction 8 over 4 End Fraction equals Start Fraction 12 over 6 End Fraction

168=2412 only
Start Fraction 16 over 8 End Fraction equals Start Fraction 24 over 12 End Fraction only

84=126 only
Start Fraction 8 over 4 End Fraction equals Start Fraction 12 over 6 End Fraction only

1 answer

To determine if either of the given equations is a proportion, we need to check if the two ratios on each side of the equation are equal.

  1. For the equation 168 = ?2412: We can interpret this as a proportion where we need to check if 168/2412 is equal to some other ratio. It's unclear what the values are supposed to be equated to, since there is a question mark in place of a = or a value.

  2. For the equation 84 = ?126: Similar to the first equation, we need to look at the proportions.

We can clarify the equations a bit. Let's assume you mean:

  • \( 168/2412 = ? \)
  • \( 84/126 = ? \)

Now we will evaluate both ratios and check for equality.

  1. For the first ratio:

    • \( 168/2412 \)
    • Simplifying \( 2412 \): \( 2412 = 168 \times 14.3571 \) (approximately).
    • Thus, \( 168/2412 \) does not simplify to a clear ratio equal to anything that we can derive specifically.
  2. For the second ratio:

    • \( 84/126 \)
    • We can simplify this: \( 84/126 = 2/3 \) since both can be divided by 42.

Since \( 168/2412 \) does not provide a clear rational number we can equate easily with something meaningful from the context given, while \( 84/126 \) simplifies down to a recognizable ratio.

Therefore, we can conclude that only 84 = 126 forms a proportion.

The correct response is: 84=126 only Start Fraction 8 over 4 End Fraction equals Start Fraction 12 over 6 End Fraction only